Geodesic
Group actions on the cubic tree
Journal of Algebraic Combinatorics, Tome 1 (1992) no. 3, pp. 209-218.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: It is known that every group which acts transitively on the ordered edges of the cubic tree $Gamma _{3}$, with finite vertex stabilizer, is isomorphic to one of seven finitely presented subgroups of the full automorphism group of $Gamma _{3}$-one of which is the modular group. In this paper a complete answer is given for the question (raised by Djokovi $cacute$ and Miller) as to whether two such subgroups which intersect in the modular group generate their free product with the modular group amalgamated.
Keywords: group actions, trees 
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Conder, Marston. Group actions on the cubic tree. Journal of Algebraic Combinatorics, Tome 1 (1992) no. 3, pp. 209-218. http://geodesic.mathdoc.fr/item/JAC_1992__1_3_a5/